The stability of translational motion of a solid with impacts on the horizontal plane

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• 作者：A. P. Markeev ; D. A. Sukhoruchkin
• 刊名：Doklady Physics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：61
• 期：2
• 页码：87-91
• 全文大小：465 KB
• 参考文献：1.I. G. Malkin, Theory of Motion Stability (Nauka, Moscow, 1966) [in Russian].MATH
  2.P. Appel’, Theoretical Mechanics (Fizmatgiz, Moscow, 1960), Vol. 2 [in Russian].
  3.A. P. Markeev, Izv. Akad. Nauk. Mekh. Tverd. Tela (5), 32 (1997).
  4.A. P. Markeev, Prikl. Mat. Mekh. 48, 363 (1984).MathSciNet
  5.A. P. Ivanov, Prikl. Mat. Mekh. 48, 725 (1984).
  6.A. P. Ivanov, Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela (2), 30 (1985).ADS
  7.A. P. Markeev, Vestn. Mosk. Univ., Ser. 1: Mat., Mekh. (3), 48 (1992).
  8.A. P. Markeev, Prikl. Mat. Mekh. 58 (3), 71 (1994).MathSciNet
  9.A. P. Markeev, Izv. Akad. Nauk. Mekh. Tverd. Tela (2), 37 (1996).
  
• 作者单位：A. P. Markeev (1)
  D. A. Sukhoruchkin (1) (2)
  
  1. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101/1, Moscow, 119526, Russia
  2. Moscow Aviation Institute (National Research University), Moscow, Russia
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Mechanics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1562-6903

文摘

The nonlinear problem on the orbital stability of the periodic motion of a homogeneous paraboloid of revolution above a stationary horizontal plane in a uniform gravitation field is solved. It is assumed that the plane is perfectly smooth and that the impacts of the solid on the plane are perfectly elastic. During unexcited motion, the axis of symmetry of the solid is vertical and the solid moves translationally and periodically encounters the plane. With the method of the Poincare section surfaces the problem is reduced to study of the stability of a stationary point of the self-mapping of the plane, which retains the area. The conditions for stability and instability are obtained for almost all physically permissible values of the parameters of the problem.